NDLI: Locally Convex Hypersurfaces of Negatively Curved Spaces

Content Provider	Scilit
Author	Alexander, S.
Copyright Year	1977
Description	A well-known theorem due to Hadamard states that if the second fundamental form of a compact immersed hypersurface M of Euclidean space is positive definite, then M is imbedded as the boundary of a convex body. There have been important generalizations of this theorem concerning hypersurfaces of , and , but there seem to be no versions for hypersurfaces of spaces of variable curvature, and no proofs which generalize to these spaces. Our main result is that Hadamard's theorem holds in any complete, simply connected Riemannian manifold of nonpositive sectional curvature.
Related Links	https://www.ams.org/proc/1977-064-02/S0002-9939-1977-0448262-6/S0002-9939-1977-0448262-6.pdf
Ending Page	325
Page Count	5
Starting Page	321
ISSN	00029939
e-ISSN	10886826
DOI	10.2307/2041451
Journal	Proceedings of the American Mathematical Society
Issue Number	2
Volume Number	64
Language	English
Publisher	Duke University Press
Access Restriction	Open
Subject Keyword	Mathematical Physics Negatively Curved Curved Spaces Locally Convex Hypersurfaces
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics

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Locally Convex Hypersurfaces of Negatively Curved Spaces